1.  \(xy\left(a^2+2b^2\right)-ab\left(2x^2+y^2\right)\)

\(=xya^2+2xyb^2-2abx^2-aby^2\)

\(=xya^2-aby^2-2abx^2+2xyb^2\)

\(=ay\left(ax-by\right)-2bx\left(ax-by\right)\)

\(=\left(ay-2bx\right)\left(ax-by\right)\)

2. \(xy\left(a^2+2b^2\right)+ab\left(2x^2+y^2\right)\)

\(=xya^2+2xyb^2+2abx^2+aby^2\)

\(=xya^2+aby^2+2abx^2+2xyb^2\)

\(=ay\left(ax+by\right)+2bx\left(ax+by\right)\)

\(=\left(ay+2bx\right)\left(ax+by\right)\)

a: Ta có: \(\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)+1\)

\(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\)

\(=\left(x^2+9x\right)^2+38\left(x^2+9x\right)+360+1\)

\(=\left(x^2+9x\right)^2+2\cdot\left(x^2+9x\right)\cdot19+19^2\)

\(=\left(x^2+9x+19\right)^2\)

b. \(x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)

\(=\left(x^2+2x+1\right)+2\left(x+1\right)\left(y+1\right)+\left(y^2+2y+1\right)\)

\(=\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\)

\(=\left(x+1+y+1\right)^2=\left(x+y+2\right)^2\)

c. \(x^2-2x\left(y+2\right)+y^2+4y+4\)

\(=x^2-2x\left(y+2\right)+\left(y+2\right)^2\)

\(=\left(x-y-2\right)^2\)

d. \(x^2+2x\left(y+1\right)+y^2+2y+1\)

\(=x^2+2x\left(y+1\right)+\left(y+1\right)^2\)

\(=\left(x+y+1\right)^2\)

1. Ta có: \(3xy\left(a^2+b^2\right)+ab\left(x^2-9y^2\right)\)

\(=3xya^2+3xyb^2+abx^2+ab9y^2\)

\(=\left(3xya^2+abx^2\right)+\left(3xyb^2+ab9y^2\right)\)

\(=ax\left(3ya+bx\right)+3by\left(xb+3ya\right)\)

\(=\left(3ya+xb\right)\left(3yb+ax\right)\)

2.Check lại đề hộ mình nha:((

Câu 2 nên sủa lại đề nha

2. xy(a²+2b²)+ab(2x²+y²)

=xya²+xy2b²+ab2x²+aby²

=(xya²+aby²)+(xy2b²+ab2x²)

=ay(ax+by)+2bx(by+ax)

=(ax+by(ay+2bx)

a. \(\left(3b+\dfrac{5a}{6}\right)^2\)

= \(9b^2+15ab+\dfrac{25a^2}{36}\)

b. (5x - y)²

= 25x² - 10xy + y²

c. (2a + b - 5)(2a - b + 5)

= 4a² - (b - 5)²

d. \(\left(x^2+\dfrac{2}{5y}\right)\left(x^2-\dfrac{2}{5y}\right)\)

= \(x^4-\dfrac{4}{25y^2}\)

a) \(2x^2+2b^2=x^2+b^2+x^2+b^2=x^2+2xb+b^2+x^2-2xb+b^2=\left(x+b\right)^2+\left(x-b\right)^2\)

WTF đăng một loạt vầy ai dám làm @@

Mấy bài này trong sách bài tập cx có bài mẫu

tự lật sách ra học ik , đăng 1 loạt ai giải cho chép zô hết

a: =(16x+20)^2-(10x+10)^2

=(16x+20-10x-10)(16x+20+10x+10)

=(26x+30)(6x+10)

=4(13x+15)(3x+5)

b: =(x-y+4-2x-3y+1)(x-y+4+2x+3y-1)

=(-x-4y+5)(3x+2y+3)

c: =[(x+1)^2-(x-1)^2][(x+1)^2+(x-1)^2]

=(x^2+2x+1-x^2+2x-1)(x^2+2x+1+x^2-2x+1)

=2(x^2+1)*4x

=8x(x^2+1)

1)

\(=x^2-4x+4+y^2+2y+1\)

\(=\left(x-2\right)^2+\left(y+1\right)^2\)

2)

\(=a^2+2ab+b^2+a^2-2ax+x^2\)

\(=\left(a+b\right)^2+\left(a-x\right)^2\)

3)

\(=x^2-2x+1+y^2+6y+9\)

\(=\left(x-1\right)^2+\left(y+3\right)^2\)

4)

\(=x^2-2xy+y^2+x^2+10x+25\)

\(=\left(x-y\right)^2+\left(x+5\right)^2\)

5)

\(=a^2+2ab+b^2+4b^2+4b+1\)

\(=\left(a+b\right)^2+\left(2b+1\right)^2\)

1/ x² - 4x + 5 + y² + 2y 

= ( x² - 4x + 4 ) + ( y² + 2y + 1 )

= ( x - 2 )² + ( y + 1 )²

2/ 2a² + 2ab - 2ax + x² + b²

= ( a² + 2ab + b² ) + ( x² - 2ax + a² )

= ( a + b )² + ( x - a )²

3/ x² - 2x + y² + 6y + 10

= ( x² - 2x + 1 ) + ( y² + 6y + 9 )

= ( x - 1 )² + ( y + 3 )²

4/ 2x² + y² - 2xy + 10x + 25

= ( x² - 2xy + y² ) + ( x² + 10x + 25 )

= ( x - y )² + ( x + 5 )²

5/ a² + 2ab + 5b² + 4b + 1

= ( a² + 2ab + b² ) + ( 4b² + 4b + 1 )

= ( a + b )² + ( 2b + 1 )²